The answer to this question may seem to be obvious -it is the RE who does the IVF treatment, of course !
Actually, while REs are the technical experts on IVF, I feel the true experts are the infertile couples who have actually gone through an IVF cycle and are willing to share their experiences and expertise with other couples. While they may not be as technically savvy as the IVF doctor, they are often much more empathetic - and far more aware of the emotional and social impact of IVF treatment.
In our modern world , it is because we worship technology that we take such a narrow view and value only technical expertise.
IVF is much more than the application of technological expertise to the problem of infertility - and the sooner we realise this and respect patients for their expertise, the better !